Graph Embeddings: Theory meets Practice

• Applicant: Professor Dr. Christopher Morris
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Theoretical Computer Science
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 468502433

Graph, network, or relational-structured data is ubiquitous across application domains ranging from chemo- and bioinformatics, combinatorial optimization to image and social network analysis. To develop successful machine learning algorithms or apply standard data analysis tools in these domains, we need techniques that map the rich information inherent in the graph structure to a vectorial representation in a meaningful way, so-called graph embeddings. Designing such embeddings comes with unique challenges. The embedding must account for the complex structure of (real-world) networks and additional high-dimensional continuous vectors attached to nodes and edges in a (permutation-)equivariant way while being scalable to massive graphs or sets of graphs. Starting from the late 1940s in chemoinformatics, different research communities have worked in the area under various guises, often leading to recurring ideas. Moreover, triggered by the resurgence of (deep) neural networks, there is an ongoing trend in the machine learning community to design permutation-equivariant neural architectures that can deal with graph- and relational input, both (semi-)supervised and unsupervised, often denoted as graph neural networks. Although successful in practical settings, most of these developments are driven by intuition and empiricism and are geared towards specific application areas. Therefore, my research objectives are centered around a more fine-grained understanding of graph embeddings' mathematical underpinnings triggered by practical applications. I want to precisely understand the trade-off in scalability and expressivity and the role of graph structure in generalization. Concurrently, I want to derive easy-to-understand guidelines and mathematical tools to customize the methodological insights for specific application domains focusing on combinatorial optimization.

• DFG Programme: Independent Junior Research Groups